How can I align vertices to an axis?
It's annoying that, in Edit Mode, Blender's Snap To : Increment doesn't have a Snap With option, otherwise this would be more intuitive.
In this case, if you have the shipped add-on  '3D View: Pie Menus' activated with the 'Origins' option, you can quickly set the origin of your object to the vertices of the desired mirror-plane from Edit Mode, and the mirrored half will jump to the original. Then you can AltG reset the object back to World 0.
But personally, rather than puzzle over each case, for more CAD-like snapping, my habit is to create temporary snap targets.

With snapping nearly always set to To : Vertex and With : Active, and the pivot set to 3D Cursor:

ShiftDX duplicate a single vertex..
SX0 scale the vertex to 0
Select the source vertex, (it will stay active), and L all the connected ones
GX Move the selected vertices, snapping to the temporary target
Delete, or merge, the target.

I wouldn't claim this is necessarily the quickest for this case, but the method is quite general. You can leave your pivot and snap settings as they are over most operations, and the sequence goes into muscle-memory.